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   "id": "73bd968b-d970-4a05-94ef-4e7abf990827",
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   "source": [
    "Chapter 02\n",
    "\n",
    "# 标量乘法\n",
    "Book_4《矩阵力量》 | 鸢尾花书：从加减乘除到机器学习 (第二版)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9fcf085a-8ecf-4003-b0b1-76f2e95c1063",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "此代码定义了一个二维列向量 $a$，其值为：\n",
    "\n",
    "$$\n",
    "a = \\begin{bmatrix} 2 \\\\ 2 \\end{bmatrix}\n",
    "$$\n",
    "\n",
    "接下来，代码通过数乘操作生成两个新向量 $b$ 和 $c$。具体而言，$b$ 是 $a$ 的 2 倍：\n",
    "\n",
    "$$\n",
    "b = 2 \\times a = 2 \\times \\begin{bmatrix} 2 \\\\ 2 \\end{bmatrix} = \\begin{bmatrix} 4 \\\\ 4 \\end{bmatrix}\n",
    "$$\n",
    "\n",
    "$c$ 是 $a$ 的 $-1.5$ 倍：\n",
    "\n",
    "$$\n",
    "c = -1.5 \\times a = -1.5 \\times \\begin{bmatrix} 2 \\\\ 2 \\end{bmatrix} = \\begin{bmatrix} -3 \\\\ -3 \\end{bmatrix}\n",
    "$$\n",
    "\n",
    "此过程展示了向量的数乘操作，通过将标量与向量相乘来改变向量的大小和方向。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f2b0f70-8b54-49c7-a58c-736dd1838f39",
   "metadata": {},
   "source": [
    "## 导入所需库"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "457dd7c5-1ef8-4272-9608-01802512d831",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np  # 导入NumPy库，用于数值计算"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2882d5b-db0c-4d22-96ba-76123168e589",
   "metadata": {},
   "source": [
    "## 定义一个列向量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "dc48b150-34ed-4cc8-a5c3-ae59f58fbcdf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2],\n",
       "       [2]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([[2], [2]])  # 定义向量a，值为[2, 2]\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e89b43f-c8e1-4af6-a3aa-eb966479608b",
   "metadata": {},
   "source": [
    "## 进行向量的数乘"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "352700c8-fc4c-4b7c-8f8b-2ee1a5905878",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4],\n",
       "       [4]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = 2 * a  # 计算b，为向量a的2倍\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a7e94dac-9695-4bcc-b09b-3dc7e823fe3b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-3.],\n",
       "       [-3.]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = -1.5 * a  # 计算c，为向量a的-1.5倍\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "85a80909-2aac-49ed-bb7a-f8cc6b80ee7d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
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   "cell_type": "code",
   "execution_count": null,
   "id": "ecd322f4-f919-4be2-adc3-69d28ef25e69",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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